Project Summary In recent years new data and technologies have transformed our understanding of transcriptional processes and how they are influenced by genetic variation. The GTEx project has measured both genetic variation and transcriptional variation in 50 tissues across hundreds of individuals, and identified hundreds of thousands of genetic variants that are associated with gene expression (eQTLs). And technological innovations have now made it possible to interrogate transcription, genome-wide, in single cells. The Human Cell Atlas (HCA) project is currently using such technologies to profile millions of cells, with the ambitious goal of providing a comprehensive atlas of the diverse cell types that make up human bodies. However, current analytic tools are limited in their ability to fully exploit the richness of these data. Current analysis tools for identifying eQTLs across 50 tissues perform well for identifying associations ? both tissue- specific effects and those that are broadly shared across tissues ? but are not yet designed for fine-mapping the underlying functional variants that explain these association signals. And methods for summarizing and characterizing transcriptional heterogeneity among single cells are not capable of capturing the complex layered character of this heterogeneity - for example, that cells might cluster into different groups depending on which genes or transcriptional processes are considered. Here we propose to develop novel statistical methods to address these issues. We will develop dimension reduction techniques for single cell analysis, aimed at capturing the complex patterns of heterogeneity that existing methods ignore. We will develop statistical tools for reliably assessing the genes and processes that show transcriptional differences among groups of cells. And we will develop and apply methods to fine-map the functional variants underlying many of the eQTLs in the GTEx project data, fully exploiting the information in the many tissues profiled, and disseminate the results on the internet in a convenient form. The overall goal of the project is to build and apply methods and software to help fully exploit the rich information in projects like GTEx and HCA, and make them available to the broad community of biological and medical scientists who can benefit from the results.